The polarization puzzle
Get two old (or cheap) pairs of polaroid sun glasses and separate all four lenses from the frames.
Call them A, B, C and D. The order doesn't matter.
Throw away D. You won't need it in this experiment.
Line up A and B so you can see a light source (an open window will do fine) through both of them.
Rotate either A or B until the light source can no longer be seen. It is "cancelled out".
Place C between A and B and the light source once again becomes visible.
Why is that? Adding that extra lens should remove transmitted light, not add some more.